Almost Orthogonal Submatrices of an Orthogonal Matrix

On the optimal correction of inconsistent matrix equations $AX = B$ and $XC = D$ with orthogonal constraint

This work focuses on the correction of both the coecient and the right hand side matrices of the inconsistent matrix equations $AX = B$ and $XC = D$ with orthogonal constraint. By optimal correction approach, a general representation of the orthogonal solution is obtained. This method is tested on two examples to show that the optimal correction is eective and highly accurate.

On the Nonsingularity of Principal Submatrices of a Random Orthogonal Matrix

Let S be a random nonnegative definite matrix and let G be an orthogonal matrix such that S = GDG', where D is the diagonal matrix of the latent roots of S. In this note, we prove _ r G t t Gt21 the a.s. existence of G~I, where G-tc2~ c=j, under some weak conditions on the distribution of S. AMS Subject Classification: Primary 62H10, 60D05.

On absolute generalized Norlund summability of double orthogonal series

In the paper [Y. Okuyama, {it On the absolute generalized N"{o}rlund summability of orthogonal series},Tamkang J. Math. Vol. 33, No. 2, (2002), 161-165] the author has found some sufficient conditions under which an orthogonal seriesis summable $|N,p,q|$ almost everywhere. These conditions are expressed in terms of coefficients of the series. It is the purpose ofthis paper to extend this result...

Discrete Sampling and Interpolation: Orthogonal Interpolation for Discrete Bandlimited Signals

We study the problem of finding unitary submatrices of the discrete Fourier transform matrix. This problem is related to a diverse set of questions on idempotents on ZN , tiling ZN , difference graphs and maximal cliques. Each of these is related to the problem of interpolating a discrete bandlimited signal using an orthogonal basis.

Construction of Compactly Supported Nonseparable Orthogonal Wavelets of L^2(R^n)